Digital FM synthesizer for record circuitry

ABSTRACT

A digital synthesizer for record circuitry of, e.g., a VCR, is supplied with digital samples representing a video signal. A calculator stage, responsive to the digital samples calculates a sequence of pulse periods defining a pulse duration modulated signal that represents FM modulation of a carrier by the video signal. An output sample generating stage operates on the sequence of pulse periods for generating a sequence of digital output samples which is converted in a digital-to-analog converter to the FM modulated video signal for subsequent recording on tape.

This is a continuation of application Ser. No. 927,512, filed asPCT/US91/03811, Jun. 30, 1991, now U.S. Pat. No. 5,390,213.

This invention relates to digital FM recording of a signal, such as thedigital recording of an FM video signal

BACKGROUND

Analog generation of an FM video signal for recording presents variousproblems, including aging of components, tolerances in the circuitrygenerating the carrier and the carrier deviation, and pre-emphasiscircuitry which vary significantly from the nominal. Digital FMmodulating techniques have, heretofore, been cumbersome requiring theuse of a substantial amount of circuitry and excessive memory storage.

A feature of the invention is a digital synthesizer technique and systemwhich avoids the disadvantages of analog modulation, without introducingthe complexity of typical digital signal processing.

SUMMARY

A digital synthesizer generates a sequence of digital output samplesrepresenting modulation of a carrier by an input signal. The synthesizeris supplied with digital input samples representing the input signal. Acalculator stage, responsive to the digital input samples calculates asequence of pulse periods defining a pulse duration modulated signalthat represents the modulation of the carrier by the input signal. Anoutput sample generating stage operates on the sequence of pulse periodsfor generating the sequence of digital output samples representing thecarrier modulated output signal.

BRIEF DESCRIPTION OF THE DRAWING

FIGS. 1a and 1b illustrate exemplary waveforms of a modulating inputsignal and a corresponding modulated output signal, respectively,including representative digital samples in both signals, derived inaccordance with inventive aspects;

FIG. 2 illustrates a flowchart of an inventive method used to calculatethe pulse periods of the FM modulated signal illustrated in FIG. 1b;

FIG. 3 illustrates a flowchart for calculating FM output samples fromthe calculated values of the FM signal pulse periods; and

FIG. 4 illustrates in block diagram form an FM record system whichincorporates an inventive digital FM synthesizer technique.

DESCRIPTION OF THE INVENTION

In an FM modulated system, the FM modulated output signal, FM(t), may bedefined as

    FM(t)=sin {2π*Freq(t)t}                                 Eq. (1),

where an instantaneous frequency, Freq(t), may be defined by

    Freq(t)=CAR+DEV*M(t)                                       Eq. (2),

where M(t) is the modulating signal, CAR is the carrier frequency, andDEV is the deviation.

The solid line waveform of FIG. 1a illustrates the waveform of anexemplary video signal, V(t), such as a luminance signal, that is to beFM modulated onto a carrier prior to recording. The solid line waveformof FIG. 1b illustrates the resultant FM modulated signal, FM(t).

A digital synthesizing technique according to the invention may be usedto generate FM(t) from V(t). The synthesis method interprets the FMsignal as a pulse duration modulated signal. That is to say, the FMoutput signal of FIG. 1b may be considered as a pulse sequence. 1,2,3, j. . . , each pulse having a period, T(j), that is determined by themodulating video signal V(t), and by the various FM system parameterssuch as carrier frequency, CAR, and deviation. DEV. Additionally, thesignal may be considered a bipolar one, in the sense that the pulsesalternate in polarity.

To ascertain the value of each pulse period T(j) using a closed formequation is possible for only a few simple modulating signals. Ingeneral, the modulating video signal V(t) is much too complex for closedform expression.

Advantageously according to an inventive arrangement of a digitalsynthesizing technique, one need consider only the average frequency,Freq_(AV), of FM(t) over an interval Δt. Taking Equation (2) intoaccount, the average frequency. Freq_(Av), may be defined as

    Freq.sub.AV =CAR+DEV*V.sub.Av                              Eq.(3)

, where ##EQU1## , i.e. V AV is the average value of the modulatingvideo signal V(t) over the interval Δt.

Because the amplitude of the FM modulated output signal, FM(t), of FIG.1b is constant, only the frequency, i.e. the time T(j) between zerocrossings, is the variable of importance. For this reason, the smallesttime interval, Δt, to consider in evaluating Equations (3) and (4), forany given pulse j, is,the corresponding pulse period T(j).

In accordance with an inventive feature, the calculation of theintervals T(j) is greatly simplified by providing discrete time samples.s(i)=s1, s2, s3 . . . of the modulating video signal V(t), havingcorresponding sampled values V1, V2, V3, . . . , as illustrated in FIG.1a, The minimum rate. 1/τ_(S), is determined by the Nyquist criterion inaccordance with the highest frequencies of the video signal V(t) thatare to be recorded, e.g. 3 megahertz in a VHS system. Advantageously,this rate, which establishes the sampling speed requirements of theanalog-to-digital converter, may be significantly lower than the outputsample rate of the FM modulated signal that is applied to thedigital-to-analog converter.

Note that the number of samples, K(j), that occur within any givenoutput pulse period T(j) varies as the frequency of the FM modulatedsignal FM(t) varies. Thus, as illustrated in FIGS. 1a and 1b, the numberof samples in the pulse period T(2) is K(2)=2, while the number ofsamples in the interval T(4) is K(4)=3.

To calculate a given pulse period T(j) from the sampled values of themodulating video signal V(t), one may use Equations (3) and (4), toequate the reciprocal of the pulse period to twice the averagefrequency, Freq_(AV), when averaged over that pulse period, i.e. whenaveraged over the time Δt=T(j). Thus

    1/T(j)=2*Freq.sub.AV (Δt=T(j))                       Eq. (5)

By having available discrete samples of the modulating signal. Theintegral expression used in calculating the average modulating signalV_(AV) of Equation (4) may be approximated by a piecewise summation overthe interval T(j). When this done, the average modulating signal may betaken as, V_(AV)Σ (j), over the interval T(j), resulting in

    1/T(j)=2*(CAR+DEV*V.sub.AVΣ (j))                     Eq. (6)

where ##EQU2## and

    τ.sub.Σ (j)=τ.sub.R (j)+τ.sub.S *(k(j)-1)+τ.sub.L (j)Eq. (8)

; where, in accordance with the notations shown in FIGS. 1a and 1b,

V(j,n)=the n-th sampled value within a given pulse period T(j), of thebaseband modulating video signal V(t), where n is a counter index,initially set equal to 1;

K(j)=the number of samples in the output pulse period T(j);

τ_(R) (j)=the residual time from the first (left-most) zero crossingpoint of the continuous-time FM modulated output signal FM(t) of a givenpulse period T(j) to the time of the first sampled value, V(j,n=1), ofthe modulating video signal within that period;

τ_(L) (j)=the time from the last sampled value, V(j,K(j)), of themodulating video signal within the period T(j) to the second(right-most) zero crossing point of FM(t) of that period;

τ_(S) =the sampling period of the baseband modulating video signal V(t).

As an example, take the 4th pulse period T(j=4) of FIGS. 1a and 1b. Foursampled values of video signal V(t) are needed. Three of the sampledvalues, V(4,1). V(4.2), and V(4,3), are found in the 4th interval, (Kequals 3), and the remaining sampled value is the last sampled value ofthe previous pulse period, sample V(3,2).

The average value V_(AV)Σ of the modulating video signal in the 4thpulse period is computed in accordance with Equation (7): ##EQU3##

A difficulty arises when one attempts to use Equations (6), (7) and (8)to calculate a sequence of output pulse periods T(j) of FIG. 1b, givenonly the sequence of input samples s(i) of the modulating, video signalV(t) in FIG. 1a. To directly calculate a given pulse period T(j) usingthese equations requires a priori knowledge of the end point of theperiod itself and a knowledge of the total number of samples K(j) ofV(t) falling within that period.

To overcome this difficulty, an iterative process is used whichmaintains a running, average period, t_(avg) (j,h), over the first hsamples occurring in a given pulse j. Initially h is set to 1 at thebeginning of the calculation of a given pulse period T(j), and is thenincremented by 1 to include another sample for use in another iterationwhen a new value of the running average period t_(avg) (j,h) iscalculated.

This procedure is repeated until the inclusion of another samplinginterval τ_(S) results in the total time, t_(sum) +τ_(S), exceeding therunning average period t_(avg) (j,h), where t_(sum) is calculated fromthe beginning-point zero crossing of the pulse to the time of thecurrent input sample. This indicates that by adding an additional sampleinterval, the end-point zero crossing of the current pulse period hasbeen exceeded. From this fact, one may conclude that the current valueof the running average period, t_(avg) (j,h), equals the pulse periodT(j), and that the total number of samples K(j) in the pulse periodequals the current value of h.

To calculate the running average period t_(avg) (j,h), consider the factthat Equations (6), (7) and (8), are valid expressions (once certainvariables are suitably redefined) for any number of samples h. Thus oneobtains ##EQU4## where τ_(R) (j)=the residual time, if any, that ispresent from the last zero crossing of the continuous-time output signalto the first output sample point in the current output interval;

h=the remaining time in the current output interval;

h=a counter index number indicating the number of input samples of V(t)found in the current output interval;

In order to simplify notation, introduce the running time variable

    τ.sub.SUM (j,h-1)=τ.sub.R (j)+(h-1)*τS         Eq.(11)

, used to determine if enough discrete-time has passed to complete afull pulse period T(j), and further introduce the variable ##EQU5##

The variable V_(AVG) (j,h-1) may be viewed as an average value of themodulating signal V(t), averaged in time from the beginning of the pulseperiod to a point that ends at sample h-1, i.e. averaged in time overthe time τ_(SUM) (j,h-1). This is illustrated in FIG. 1a, for the 4thpulse period that contains input samples s7, s8 and s89, preceded by thesample s6, the last sample of the previous pulse period.

Assume that the iterative process has proceeded to the point whereτ_(SUM) and V_(AVG) have been calculated using the samples throughsample h-1=2, i.e., through the 2nd sample, sample s8. Based on Equation(11), the accumulated running time, τ_(SUM) (4,2), from the beginning ofthe 4th pulse interval to the 3rd sample s9, is equal to τ_(R)(4)+2τ_(S). The discrete-time average value V_(AVG) (4,2) of themodulating signal averaged over the accumulated running time is thetotal of the 3 areas shown in hatching in FIG. 1a divide by τ_(SUM). Thesample values used in the calculation includes the last sample, s6, inthe previous pulse period, as well as the first two samples, s7 and s8,in the current period.

Once V_(AVG) has been calculated, the running average period τ_(avg)(j,h) may be obtained in the following manner. Equation (10) may berewritten as ##EQU6##

The discrete-time average value V_(AVG) was calculated using arectangular approximation of V(t) between two actual sample points.Other approximations, such as a straight line connection between twosample points, may be used, at the possible expense of having a morecomplicated calculation algorithm.

It is important to note that a zero crossing of the output signal mustoccur when τSUM>t_(avg). The instantaneous frequency is not knownexactly until this condition is met. It is possible however to determineif a zero crossing should occur between two sample times t=t₁ and t=t₁+τ_(S) by evaluating t_(avg) at t=t₁. For example, in FIGS. 1a and 1b, azero crossing occurs between samples s9 and s10. To determine that sucha zero crossing has occurred, it is necessary to note that

    τ.sub.L (j,h)=t.sub.avg (-j,h)-τ.sub.SUM (j,h-1)   Eq. (14)

, resulting in ##EQU7##

Thus at any value of h, the values of τ_(SUM) (j,h-1), V_(AVG) (j,h-1)and t_(avg) (j,h) can be calculated from the sampled input, given thatCAR and DEV are known numeric constants. It should be noted that thereare no input sample values which can cause t_(avg) (j,h) to be less thanτ_(R) (j)+τ_(S).

After t_(avg) (j,h) is calculated, it is necessary to determine whetheror not t_(avg) (j,h)>τ_(R) (j)+(h-1)τ_(S). If it is greater, then a newvalue of τ_(SUM) and V_(AVG) is calculated and h is incremented by 1.

If τ_(SUM) (j,h-1)+τS>t_(avg) (j,h), then it is necessary to store 3values in an output memory queue. These are t_(avg) (j,h)=T(j), h=K(j)and the residual time τ_(R) (j). These values are used in conjunctionwith a relatively small capacity sine ROM lookup table to calculatediscrete-time values of the FM modulated output signal, as will be laterdescribed.

To calculate the next pulse period T(j+1), it is necessary to calculatea new value of the residual time, τ_(R) (j+1), for the next outputpulse, pulse j+1. The new value is τ_(R) (j+1)=τ_(SUM) (j,h-1)+τ_(S)-T(j). After the new value of τ_(R) (j+1) is calculated, h is resetto 1. However, if τ_(R) is ever 0, for example, if τ_(R) (j+1)=0 then his set to 2. After these data updating steps have been performed. Theprocess of evaluating the next running average period t_(avg) (j+1,h) isthen initiated.

A flowchart describing the above procedure is given in FIG. 2. It shouldbe noted that for initialization purposes the first output pulse, pulsej=1 of FIG. 1b, is arbitrarily chosen as a positive pulse and phasedrelative to the first input sample s1 so as to set the first residualtime τ_(R) (j=1)=0. Any subsequent residual time can then be determinedonce its preceding pulse period has been calculated.

Discrete-time values, FM(j,n), of the FM modulated output signal, shownin FIG. 1b, may be calculated for each pulse j, based on the values ofT(j), τ_(R) (j) stored in the output memory queue. The equation forFM(j,n) is ##EQU8## for n=1,2, . . . , K(j), and where SGN(j) is thesign function, i.e. (-1) raised to the j-th power. The change inpolarity of alternate output pulses introduced by the sign function isindicative of the quantization of the output signal.

The values of FM(j,n) are then supplied to a digital-to-analog converterfor generating the continuous-time FM modulated output signal FM(t) ofFIG. 1b.

It may be advantageous to operate the digital-to-analog converter in themodulator output stage at a faster rate, 1/τ_(DA), than the rate, τ_(S),for which input samples s(i) are being generated. Equation (16) is thenmodified to the following ##EQU9## for p=0.1,2, . . . . The time τ₀ (j)represents the residual time between the first zero crossing instant ofthe j-th output pulse and the occurrence of the first computed outputsample FM(j,0) in that pulse period. For initialization purposes, theresidual time τ₀ (1) of the first pulse is set to 0.

When the counter variable p has been incremented to the point where anew pulse period is being entered, a new value T(j+1) for the nextoutput pulse period is fetched from memory. The counter variable p isreset to 0 before beginning the calculation of a new sequence of outputsamples in the pulse period j+1. Storing in memory of the calculatedvalues τ_(R) (j) and K(j) is unnecessary since they are not being usedfor the calculation of the output samples FM(j,p). A flowchart of thesteps taken to calculate the sequence of output samples FM(j,p) isprovided in FIG. 3.

The digital FM synthesizing technique just described, in accordance withvarious inventive aspects, may be used to record an input signal on arecording medium. For example, this technique may be used to record aluminance, chrominance, or composite video signal on video tape.

The circuit is compatible with all FM record standards (NTSC, PAL andSECAM for VHS or SVHS), with the only restriction being the samplingrate of the A/D and the conversion rate of the D/A. This greatly reducesthe parts count external to the IC's in, e.g., a multistandard recorder.

A block diagram of a VCR record system 30, including a digital FMsynthesizer 10 embodying the invention, is shown in FIG. 4. The clockinput to the digital part of the system, fck, is greater than 25megahertz for PAL in the SVHS standard and is approximately 20 megahertzfor PAL in the VHS standard. A low pass filter 11 may be used toeliminate frequencies in the input signal Vin above the Nyquistfrequency of analog-to-digital converter, A/D 12 (10 megahertz). The A/Dcould actually operate at approximately 10 megahertz clock frequency,f1, for video applications without loss of signal fidelity. Input signalVin may be, illustratively, an analog baseband luminance signal.

A pre-emphasis filter 13 receives the digitized input signal. The filtermay be constructed as a standard Infinite Impulse Response or FiniteImpulse Response digital filter which approximates the pre-emphasisfunction for the recording system being used (1.3 microsecond for PALVHS).

The output of pre-emphasis filter 13 is applied to a clipping circuit14, which is used to limit the minimum and maximum frequency of theoutput FM signal. This is easily implemented with a lookup table on theoutput data from the digital filter section. This assumes that videoclamping and AGC are applied to the signal, by circuitry not shown,prior to filtering. Other conventional processing of the signal prior toentering the modulator stage are also omitted from the figure.

A digital FM modulator 15, embodying the invention, receives the digitalsamples s(i) from the output of clipping circuit 14 and generatesdigital FM output samples, FM(j,n) or FM(j,p), calculated in accordancewith the digital synthesizing techniques described above. The digital FMmodulator stage is similar in concept to an IIR filter because it uses agroup of time domain samples to calculate the output signal. Thisimplies a fixed delay from the input to the output.

Modulator 15 is arranged in three stages. The first stage 16 receivesthe digital input samples s(i) and calculates the sequence of outputpulse periods T(j) and the associated sequences for the residual timesτ_(R) (j) and the sample counts K(j). The second stage 17, a memorystage, stores the values of T(j), τ_(R) (j) and K(j). These values arethen fetched by the last stage 18, the FM modulator stage, to generatethe sequence of digital FM modulated output samples FM(j,n).

Memory stage 17 functions as a first-in-first-out, FIFO, queue. Thequeue prevents the output calculator in FM modulator stage iS fromrunning out of values of T(j), τ_(R) (j) and K(j) when the currentoutput frequency is higher than the next, i.e. during a maximum white tomaximum black transition. If modulator stage 18 calculates the outputsamples as samples FM(j,p), in accordance with the algorithm of theflowchart of FIG. 3, then memory stage 17 need store only the values ofT(j).

A digital-to-analog converter, D/A 19, operating at an output clock ratef2, converts the FM output samples from modulator stage 18 into ananalog signal FM(t). The FM signal is then sent to the VCR recordelectronics stage 20 for recording the signal on magnetic tape.

If the modulator stage operates at an output rate that is higher thanthe input sampling rate f1, e.g. at the D/A conversion rate f2, then theoutput rate must exceed 2*(CAR+f_(max) +DEV/2), where f_(max) is themaximum frequency of the input modulating signal. There need be nodirect relationship between the input sampling rate f2 and the FM outputconversion rate. This permits the use of an existing clock that isavailable in the VCR, e.g. of a clock operating at 4Fsc=17.734476megahertz, when processing a PAL video signal.

Because the input sampling rate and the output conversion rate need notbe directly related, the calculations of the pulse periods T(j) may beperformed at a comparatively low frequency (6-7 megahertz) while theoutput converter runs at a high frequency (4 times the input rate). Thishas two advantages. The more complex stage which calculates the pulseperiods may be implemented with higher resolution in order to preservesignal accuracy and fidelity. The output sine table, adders and D/A's donot require as much accuracy due to the oversampling of the sinefunction. This reduces the complexity of the hardware required toimplement the modulator.

The arrangements described above advantageously minimize calculationtime, minimize the required memory space, and minimize the requiredanalog bandwidth. Close tolerances are maintained on the carrier anddeviation, to within the tolerances of the various clocks used by thesystem. Low input sampling rates and output D/A conversion rates areused, typically digital video rates. No external analog adjustments arerequired, resulting in minimal drift with aging, according to the clockdrifts. Few unit-to-unit variations in pre-emphasis are found, andrecord format changes under software control is made possible.

What is claimed:
 1. Apparatus, comprising:first means for providing afirst plurality of digital samples representative of an input signal;second means coupled to said first means for generating a secondplurality of digital samples which represents a corresponding pluralityof pulse periods that defines a pulse duration modulated signalrepresenting modulation of a carrier by said input signal; and thirdmeans responsive to said second plurality of digital samples forgenerating a third plurality of digital samples representing a modulatedoutput signal corresponding to said pulse duration modulated signal. 2.The apparatus of claim 1 further comprising electronic recording meansresponsive to said third plurality of digital samples, for recording ona recording medium a signal representative of said output signal.
 3. Theapparatus of claim 2 wherein said recording medium is video tape.
 4. Theapparatus of claim 3 wherein said input signal includes luminanceinformation.
 5. The apparatus of claim 1 wherein said third meansgenerates said third plurality of digital samples representing asequence of output pulses having pulse widths corresponding to saidpulse periods.
 6. The apparatus of claim 5 wherein said sequence ofoutput pulses is a sequence of pulses which alternate in polarity. 7.The apparatus of claim 1 wherein said third plurality of digital samplesrepresents an FM carrier modulated output signal.
 8. The apparatus ofclaim 7 wherein said third plurality of digital samples is a sequence ofpulses which alternate in polarity.
 9. The apparatus of claim 1 furtherincluding a digital-to-analog converter responsive to said thirdplurality of digital samples for generating said modulated output signalas an analog output signal.
 10. The apparatus of claim 9 furtherincluding record electronics for recording said analog output signal ona recording medium.
 11. The apparatus of claim 10 wherein said recordingmedium is video tape.
 12. The apparatus of claim 11 wherein said inputsignal comprises a luminance signal.
 13. The apparatus of claim 12wherein said modulated output signal is a frequency modulated signal.14. The apparatus of claim 9 wherein said input signal is an analogsignal and said first means comprises an analog-to-digital converterresponsive to said analog input signal for providing said firstplurality of digital samples at an output thereof.
 15. The apparatus ofclaim 14 wherein said analog-to-digital converter and saiddigital-to-analog converter have different sampling rates.
 16. Theapparatus of claim 14 wherein the sampling rate of saidanalog-to-digital converter is slower than the sampling rate of saiddigital-to-analog converter.
 17. The apparatus of claim 1 includingmeans for storing said plurality of pulse periods in a memory, saidthird means retrieving said stored plurality of pulse periods from saidmemory as needed, for calculation of the values of said third pluralityof digital samples.
 18. The apparatus of claim 1 wherein said pluralityof pulse periods is a sequence of pulse periods T(j), j=1,2,3, . . . ,that defines said pulse duration modulated signal representing FMmodulation of a carrier by said input signal, in accordance with theequation:

    1/T(j)=2*(CAR+DEV*V.sub.AVΣ (j)

where ##EQU10## and

    τ.sub.Σ (j)=τ.sub.R (j)+τ.sub.S *(K(j)-1)+τ.sub.L (j);

where, CAR=the FM carrier frequency; DEV=the FM deviation; V(j,n)=then^(th) one of said first plurality of digital samples within a givenpulse period T(j), where n is a counter index, initially set equal to 1;K(j)=the number of said first plurality of digital samples in the pulseperiod T(j); τ_(R) (j)=the residual time from the first zero crossingpoint of said pulse duration modulated signal of a given pulse periodT(j) to the time of the first one V(j,n=1), of said first plurality ofdigital samples within that period; τ_(L) (j)=the time from the lastone, V(j,K(j)), of said first plurality of digital samples within theperiod T(j) to the second zero crossing point of said pulse durationmodulated signal within that period; and τS=the sampling periodassociated with said first plurality of digital samples.
 19. Theapparatus of claim 18 wherein said third means generates said thirdplurality of digital samples as a sequence of digital samples, FM(j,n),in accordance with the equation ##EQU11## where SGN(j) is the signfunction.
 20. The apparatus of claim 19 including means for storing in amemory said sequence of pulse periods T(j), a sequence of correspondingvalues τ_(R) (j) and a sequence of corresponding values K(j), said thirdmeans retrieving the three stored sequences from said memory as needed,for calculation of the values of said third plurality of digitalsamples.
 21. The apparatus of claim 1 wherein said plurality of pulseperiods defines a sequence of pulse periods T(j), j=1,2,3, . . . , thatdefines said pulse duration modulated signal representing FM modulationof a carrier by said input signal, to generate said third plurality ofdigital samples as a sequence of digital output samples FM(j,p), inaccordance with the equation: ##EQU12## p=0,1,2, . . . , where τ_(DA)=the sample interval between successive ones of said digital outputsamples, andτ0(j)=the residual time between the first zero crossinginstant of an output pulse corresponding to the j^(th) pulse period andthe occurrence of the first computed output sample FM(j,O) in that pulseperiod.
 22. The apparatus of claim 21 wherein the interval τ_(DA) isshorter than the sampling period associated with said first plurality ofdigital samples.